Figure 1. Spectrometer Setup

Spectrometry Terms;

1.) Hue: color or shade. It has reddish hues. Degree to which a stimulus can be described as similar or different from described stimuli. Dependent on the dominant wavelength, independent of intensity or lightness.

2.) Chroma: the vividness or dullness of a color; how close the color is to either gray or the pure hue (red). Chroma describes how pure, or monochromatic, a color is compared to a white surface with the same illumination

3.) Saturation: the degree of purity of a hue

4.) Spectral purity: quantification of the monochromaticity of a given light sample; stability of a signal; how clean a spectrum is compared to what it should be.

5.) Brightness: measures the ability to of a sample to reflect blue light; lower brightness values mean greater pigmentation; measures the reflection of a very specific wavelength of light.

6.) Spectral Whiteness: Measures the ability to reflect all colors of light….remember things like sand reflect light; measures the reflection of all wavelengths of light across the visible spectrum thus this measure is more in line without visual perception.

7.) A tint is created when any saturated hue on a spectrum is mixed with white to form a lighter color.

Figure 2. Southern Redbelly Dace (Chrosomus erythrogaster)
color_data <- read.csv("color_data.csv")
ggpairs(color_data, columns = 2:5) + theme_bw()

correlation.matrix <- cor(color_data[,2:5])
round(correlation.matrix, 2)
##                     Red_Coloration_Area Whiteness_Avg Chroma_Avg Tint_Avg
## Red_Coloration_Area                1.00         -0.72       0.70    -0.79
## Whiteness_Avg                     -0.72          1.00      -0.93     0.95
## Chroma_Avg                         0.70         -0.93       1.00    -0.96
## Tint_Avg                          -0.79          0.95      -0.96     1.00

Correlation between the variables. Anything above ~0.5 we should look at.

options(na.action = “na.fail”)

options(width = 90)

Now running lm with additive effects of the variables in relation to GSI_Value.

model_GSI1 <- lm(GSI_Value ~ Red_Coloration_Area + Whiteness_Avg + Chroma_Avg + Tint_Avg, data=color_data)
anova (model_GSI1) 
## Analysis of Variance Table
## 
## Response: GSI_Value
##                     Df Sum Sq Mean Sq F value Pr(>F)
## Red_Coloration_Area  1  21.46 21.4641  0.7686 0.3911
## Whiteness_Avg        1  12.36 12.3636  0.4427 0.5134
## Chroma_Avg           1   5.84  5.8416  0.2092 0.6523
## Tint_Avg             1   9.80  9.8043  0.3511 0.5602
## Residuals           20 558.54 27.9271
performance::check_collinearity(model_GSI1)
## # Check for Multicollinearity
## 
## Low Correlation
## 
##                 Term  VIF Increased SE Tolerance
##  Red_Coloration_Area 3.01         1.73      0.33
## 
## High Correlation
## 
##           Term   VIF Increased SE Tolerance
##  Whiteness_Avg 10.85         3.29      0.09
##     Chroma_Avg 13.57         3.68      0.07
##       Tint_Avg 23.36         4.83      0.04

Red Coloration Area has a VIF <5 showing low correlation with other predictors.

Dredge out models from the previous linear model for EXPLORATORY PURPOSE ONLY.

options(na.action = "na.fail") # otherwise blows up with NA values
dredge_GSI<-dredge(model_GSI1)
## Fixed term is "(Intercept)"
dredge_GSI
## Global model call: lm(formula = GSI_Value ~ Red_Coloration_Area + Whiteness_Avg + 
##     Chroma_Avg + Tint_Avg, data = color_data)
## ---
## Model selection table 
##    (Int)  Chr_Avg Red_Clr_Are Tnt_Avg Wht_Avg df  logLik  AICc delta weight
## 1  5.892                                       2 -75.365 155.3  0.00  0.254
## 5  8.235                      0.02747          3 -74.653 156.4  1.17  0.142
## 9  8.619                              0.02325  3 -74.660 156.5  1.19  0.140
## 3  7.488            -0.112800                  3 -74.916 157.0  1.70  0.109
## 2  8.000 -0.08171                              3 -74.933 157.0  1.73  0.107
## 6  7.336  0.20740             0.07968          4 -74.399 158.8  3.52  0.044
## 10 8.470  0.11450                     0.04717  4 -74.544 159.1  3.81  0.038
## 13 8.475                      0.01544 0.01080  4 -74.637 159.3  4.00  0.034
## 11 8.625            -0.024740         0.02032  4 -74.649 159.3  4.02  0.034
## 7  8.237            -0.002365 0.02711          4 -74.653 159.3  4.03  0.034
## 4  8.056 -0.04589   -0.069270                  4 -74.845 159.7  4.41  0.028
## 14 7.741  0.24020             0.06050 0.02463  5 -74.322 161.8  6.53  0.010
## 8  7.198  0.22880    0.044630 0.09195          5 -74.374 161.9  6.63  0.009
## 12 8.470  0.12100   -0.035610         0.04430  5 -74.522 162.2  6.93  0.008
## 15 8.494            -0.008612 0.01358 0.01128  5 -74.636 162.4  7.15  0.007
## 16 7.607  0.25670    0.037330 0.07166 0.02349  6 -74.304 165.3 10.00  0.002
## Models ranked by AICc(x)

Here we see there are 16 possible models based on additive combinations of the variables.

Let’s dredge models for a delta <2/ within two AICc units.

subset(dredge_GSI, delta <2)
## Global model call: lm(formula = GSI_Value ~ Red_Coloration_Area + Whiteness_Avg + 
##     Chroma_Avg + Tint_Avg, data = color_data)
## ---
## Model selection table 
##   (Int)  Chr_Avg Red_Clr_Are Tnt_Avg Wht_Avg df  logLik  AICc delta weight
## 1 5.892                                       2 -75.365 155.3  0.00  0.338
## 5 8.235                      0.02747          3 -74.653 156.4  1.17  0.188
## 9 8.619                              0.02325  3 -74.660 156.5  1.19  0.187
## 3 7.488              -0.1128                  3 -74.916 157.0  1.70  0.145
## 2 8.000 -0.08171                              3 -74.933 157.0  1.73  0.142
## Models ranked by AICc(x)

Model 1 is about 1.8 times more likely than model 5 and model 9 (0.338/0.188) and (0.338/0.187). Model 1 is about 2.33 times more likely than model 3 (0.338/0.145). Model 1 is about 2.38 times more likely than model 2.

*Model 5 has support for tint average, model 9 has support for whiteness average, model 3 has support for red coloration area, and model 2 has support for chroma average.

Now let’s rank variables support in the models above. This calculates variable importance weights.

importance(dredge_GSI)
##                      Tint_Avg Whiteness_Avg Chroma_Avg Red_Coloration_Area
## Sum of weights:      0.281    0.273         0.245      0.231              
## N containing models:     8        8             8          8

The results of importance show that each of the four variables show up 8 times in the models.

Based on the effects of variables in the models using subset(dredge_wash, delta <2) and some other combinations, I ran the following lm:

model1 <- lm(GSI_Value~Chroma_Avg+Red_Coloration_Area, data = color_data)
model2 <- lm(GSI_Value~Whiteness_Avg+Chroma_Avg, data = color_data)
model3 <- lm(GSI_Value~Red_Coloration_Area+Tint_Avg, data = color_data)
model4 <- lm(GSI_Value~Whiteness_Avg+Chroma_Avg+Tint_Avg, data= color_data)
model5 <- lm(GSI_Value~ Whiteness_Avg+Tint_Avg, data= color_data)
model6 <- lm(GSI_Value~ Tint_Avg, data= color_data)
model7 <- lm(GSI_Value~ Whiteness_Avg, data= color_data)
model8 <- lm(GSI_Value~Red_Coloration_Area, data= color_data)
model9 <- lm(GSI_Value~ Chroma_Avg, data= color_data)
out.put4<-model.sel(model1,model2,model3, model4, model5, model6, model7, model8, model9)
out.put4
## Model selection table 
##        (Int)  Chr_Avg Red_Clr_Are Wht_Avg Tnt_Avg             family df  logLik
## model6 8.235                              0.02747 gaussian(identity)  3 -74.653
## model7 8.619                      0.02325         gaussian(identity)  3 -74.660
## model8 7.488            -0.112800                 gaussian(identity)  3 -74.916
## model9 8.000 -0.08171                             gaussian(identity)  3 -74.933
## model2 8.470  0.11450             0.04717         gaussian(identity)  4 -74.544
## model5 8.475                      0.01080 0.01544 gaussian(identity)  4 -74.637
## model3 8.237            -0.002365         0.02711 gaussian(identity)  4 -74.653
## model1 8.056 -0.04589   -0.069270                 gaussian(identity)  4 -74.845
## model4 7.741  0.24020             0.02463 0.06050 gaussian(identity)  5 -74.322
##         AICc delta weight
## model6 156.4  0.00  0.221
## model7 156.5  0.02  0.219
## model8 157.0  0.53  0.170
## model9 157.0  0.56  0.167
## model2 159.1  2.64  0.059
## model5 159.3  2.83  0.054
## model3 159.3  2.86  0.053
## model1 159.7  3.24  0.044
## model4 161.8  5.35  0.015
## Models ranked by AICc(x)

Subset for output models, you can see that the models with one variable in them show the most support, with model 6 (y=GSI_Value and x=Tint) as the top model.

subset(out.put4, delta <2)
## Model selection table 
##        (Int)  Chr_Avg Red_Clr_Are Wht_Avg Tnt_Avg             family df  logLik
## model6 8.235                              0.02747 gaussian(identity)  3 -74.653
## model7 8.619                      0.02325         gaussian(identity)  3 -74.660
## model8 7.488              -0.1128                 gaussian(identity)  3 -74.916
## model9 8.000 -0.08171                             gaussian(identity)  3 -74.933
##         AICc delta weight
## model6 156.4  0.00  0.284
## model7 156.5  0.02  0.282
## model8 157.0  0.53  0.219
## model9 157.0  0.56  0.215
## Models ranked by AICc(x)

Model 6 is about 1 times more likely than model 7. Model 6 is about 1.30 times more likely than model 8. Model 6 is about 1.32 times more likely than model 9.

Now to average the models using the lm from out.put4

model.avg(out.put4, revised.var = TRUE)
## 
## Call:
## model.avg(object = out.put4, revised.var = TRUE)
## 
## Component models: 
## '4'   '3'   '2'   '1'   '13'  '34'  '24'  '12'  '134'
## 
## Coefficients: 
##        (Intercept)   Tint_Avg Whiteness_Avg Red_Coloration_Area   Chroma_Avg
## full      8.164763 0.00924022   0.008823809         -0.02227681 -0.005228465
## subset    8.164763 0.02699481   0.025450803         -0.08373316 -0.018382671
summary(model.avg(out.put4))
## 
## Call:
## model.avg(object = out.put4)
## 
## Component model call: 
## lm(formula = <9 unique values>, data = color_data)
## 
## Component models: 
##     df logLik   AICc delta weight
## 4    3 -74.65 156.45  0.00   0.22
## 3    3 -74.66 156.46  0.02   0.22
## 2    3 -74.92 156.97  0.53   0.17
## 1    3 -74.93 157.01  0.56   0.17
## 13   4 -74.54 159.09  2.64   0.06
## 34   4 -74.64 159.27  2.83   0.05
## 24   4 -74.65 159.31  2.86   0.05
## 12   4 -74.84 159.69  3.24   0.04
## 134  5 -74.32 161.80  5.35   0.02
## 
## Term codes: 
##          Chroma_Avg Red_Coloration_Area       Whiteness_Avg            Tint_Avg 
##                   1                   2                   3                   4 
## 
## Model-averaged coefficients:  
## (full average) 
##                      Estimate Std. Error Adjusted SE z value Pr(>|z|)   
## (Intercept)          8.164763   2.445593    2.579872   3.165  0.00155 **
## Tint_Avg             0.009240   0.029213    0.030548   0.302  0.76228   
## Whiteness_Avg        0.008824   0.027575    0.028790   0.306  0.75923   
## Red_Coloration_Area -0.022277   0.089330    0.093253   0.239  0.81119   
## Chroma_Avg          -0.005228   0.101610    0.105943   0.049  0.96064   
##  
## (conditional average) 
##                     Estimate Std. Error Adjusted SE z value Pr(>|z|)   
## (Intercept)          8.16476    2.44559     2.57987   3.165  0.00155 **
## Tint_Avg             0.02699    0.04488     0.04740   0.569  0.56903   
## Whiteness_Avg        0.02545    0.04207     0.04436   0.574  0.56612   
## Red_Coloration_Area -0.08373    0.15763     0.16595   0.505  0.61387   
## Chroma_Avg          -0.01838    0.18989     0.19804   0.093  0.92604   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Term Codes for the variables: 1 = Chroma Average, 2 = Red Coloration Area, 3 = Whiteness_Avg, and 4 = Tint_Avg. Look at component models: models 4, 3, 2, and 1 are within two AICc units. Notice interactions and additive representation of these variables leads to higher delta AICc values. The variables show high p-values. From the estimate column, we see a positive effect of Tint_avg and Whiteness_avg and a negative effect of Red Coloration Area and Chroma_avg on GSI_Value. Model 4 (y=GSI_Value and x=Tint_avg) shows most support.

w1 <- ggplot(color_data, aes(Red_Coloration_Area, GSI_Value)) + 
  geom_point() +
  geom_smooth(method="lm")

w2 <- ggplot(color_data, aes(Whiteness_Avg, GSI_Value)) + 
  geom_point() +
  geom_smooth(method="lm")

w3 <- ggplot(color_data, aes(Chroma_Avg, GSI_Value)) + 
  geom_point() +
  geom_smooth(method="lm")

w4 <- ggplot(color_data, aes(Tint_Avg, GSI_Value)) + 
  geom_point() +
  geom_smooth(method="lm")


w1 / w2 / w3 / w4
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'

Figure 4. Southern Redbelly Dace (Chrosomus erythrogaster) Body Condition Measurments

ggpairs(body_condition_color, columns = 2:5) + theme_bw()

options(na.action = “na.fail”)

options(width = 90)

Body_Condition.all.parms<-lm(Body_Condition_Factor ~ Red_Coloration_Area + Whiteness_Avg + Chroma_Avg + Tint_Avg, data = body_condition_color)
anova(Body_Condition.all.parms)
## Analysis of Variance Table
## 
## Response: Body_Condition_Factor
##                     Df   Sum Sq   Mean Sq F value Pr(>F)
## Red_Coloration_Area  1 0.000006 0.0000056  0.0009 0.9763
## Whiteness_Avg        1 0.003683 0.0036834  0.5972 0.4487
## Chroma_Avg           1 0.004704 0.0047038  0.7627 0.3929
## Tint_Avg             1 0.000162 0.0001620  0.0263 0.8729
## Residuals           20 0.123349 0.0061675
results1<-MuMIn::dredge(Body_Condition.all.parms) 
## Fixed term is "(Intercept)"
results1
## Global model call: lm(formula = Body_Condition_Factor ~ Red_Coloration_Area + Whiteness_Avg + 
##     Chroma_Avg + Tint_Avg, data = body_condition_color)
## ---
## Model selection table 
##     (Int)    Chr_Avg Red_Clr_Are    Tnt_Avg    Wht_Avg df logLik  AICc delta
## 1  0.7968                                               2 30.083 -55.6  0.00
## 9  0.7761                                   -0.0001772  3 30.268 -53.4  2.23
## 5  0.7866                        -0.0001199             3 30.144 -53.1  2.48
## 2  0.7901  0.0002596                                    3 30.103 -53.1  2.56
## 3  0.7960              5.747e-05                        3 30.084 -53.0  2.60
## 10 0.7808 -0.0036420                        -0.0009380  4 30.797 -51.6  4.03
## 13 0.7689                         0.0007699 -0.0007984  4 30.527 -51.1  4.57
## 11 0.7764             -1.463e-03            -0.0003507  4 30.438 -50.9  4.75
## 6  0.7954 -0.0020240             -0.0006294             4 30.249 -50.5  5.12
## 7  0.7878             -1.157e-03 -0.0002981             4 30.225 -50.4  5.17
## 4  0.7904  0.0004514  -3.710e-04                        4 30.114 -50.2  5.39
## 12 0.7808 -0.0034320  -1.155e-03            -0.0010310  5 30.905 -48.7  6.97
## 14 0.7791 -0.0033460              0.0001424 -0.0009910  5 30.803 -48.4  7.17
## 15 0.7705             -7.379e-04  0.0006102 -0.0007571  5 30.560 -48.0  7.66
## 8  0.8008 -0.0028630  -1.745e-03 -0.0011090             5 30.416 -47.7  7.95
## 16 0.7843 -0.0039840  -1.451e-03 -0.0002913 -0.0009466  6 30.922 -45.2 10.44
##    weight
## 1   0.354
## 9   0.116
## 5   0.103
## 2   0.099
## 3   0.097
## 10  0.047
## 13  0.036
## 11  0.033
## 6   0.027
## 7   0.027
## 4   0.024
## 12  0.011
## 14  0.010
## 15  0.008
## 8   0.007
## 16  0.002
## Models ranked by AICc(x)
subset(results1, delta <3)
## Global model call: lm(formula = Body_Condition_Factor ~ Red_Coloration_Area + Whiteness_Avg + 
##     Chroma_Avg + Tint_Avg, data = body_condition_color)
## ---
## Model selection table 
##    (Int)   Chr_Avg Red_Clr_Are    Tnt_Avg    Wht_Avg df logLik  AICc delta
## 1 0.7968                                              2 30.083 -55.6  0.00
## 9 0.7761                                  -0.0001772  3 30.268 -53.4  2.23
## 5 0.7866                       -0.0001199             3 30.144 -53.1  2.48
## 2 0.7901 0.0002596                                    3 30.103 -53.1  2.56
## 3 0.7960             5.747e-05                        3 30.084 -53.0  2.60
##   weight
## 1  0.461
## 9  0.151
## 5  0.134
## 2  0.128
## 3  0.126
## Models ranked by AICc(x)

Model 1 is about 3.05 times more likely than model 9 (0.461/0.151). Model 9 shows an effect of Whiteness_avg. Model 5 shows an effect of Tint_avg. Model 2 shows an effect of Chroma_avg. Lastly, model 3 shows an effect of Red Coloration Area.

Model 9 shows the effect of Whiteness_avg. Model 5 shows the effect of Tint_avg. Model 2 shows the effect of Chroma_avg. Model 3 shows the effect of Red_Coloration_Area.

MuMIn::importance(results1)
##                      Whiteness_Avg Chroma_Avg Tint_Avg Red_Coloration_Area
## Sum of weights:      0.263         0.226      0.219    0.207              
## N containing models:     8             8          8        8

Each variable has about the same weight. Each variable shows up in eight models.

Based on the effects of variables in the models using subset(results1, delta <3) and some other additive combinations, I ran the following lm:

mod1 <- lm(Body_Condition_Factor~Whiteness_Avg, data = body_condition_color)
mod2 <- lm(Body_Condition_Factor~Tint_Avg, data = body_condition_color)
mod3 <- lm(Body_Condition_Factor~Red_Coloration_Area, data = body_condition_color)
mod4 <- lm(Body_Condition_Factor~Chroma_Avg, data=body_condition_color)
mod5 <- lm(Body_Condition_Factor~Whiteness_Avg+Chroma_Avg+Tint_Avg, data=body_condition_color)
out.put_modelselection<-model.sel(mod1,mod2,mod3, mod4, mod5)
out.put_modelselection
## Model selection table 
##       (Int)    Wht_Avg    Tnt_Avg Red_Clr_Are    Chr_Avg             family df
## mod1 0.7761 -0.0001772                                   gaussian(identity)  3
## mod2 0.7866            -0.0001199                        gaussian(identity)  3
## mod4 0.7901                                    0.0002596 gaussian(identity)  3
## mod3 0.7960                         5.747e-05            gaussian(identity)  3
## mod5 0.7791 -0.0009910  0.0001424             -0.0033460 gaussian(identity)  5
##      logLik  AICc delta weight
## mod1 30.268 -53.4  0.00  0.274
## mod2 30.144 -53.1  0.25  0.242
## mod4 30.103 -53.1  0.33  0.232
## mod3 30.084 -53.0  0.37  0.228
## mod5 30.803 -48.4  4.95  0.023
## Models ranked by AICc(x)
subset(out.put_modelselection, delta <2)
## Model selection table 
##       (Int)    Wht_Avg    Tnt_Avg Red_Clr_Are   Chr_Avg             family df
## mod1 0.7761 -0.0001772                                  gaussian(identity)  3
## mod2 0.7866            -0.0001199                       gaussian(identity)  3
## mod4 0.7901                                   0.0002596 gaussian(identity)  3
## mod3 0.7960                         5.747e-05           gaussian(identity)  3
##      logLik  AICc delta weight
## mod1 30.268 -53.4  0.00  0.281
## mod2 30.144 -53.1  0.25  0.248
## mod4 30.103 -53.1  0.33  0.238
## mod3 30.084 -53.0  0.37  0.233
## Models ranked by AICc(x)

Model 1 is about 1.13 times more likely than model 2. Model 1 is about 1.18 times more likely than model 4. Lastly, Model 1 is about 1.2 times more likely than model 3.

Now to average the models

model.avg(out.put_modelselection, revised.var = TRUE)
## 
## Call:
## model.avg(object = out.put_modelselection, revised.var = TRUE)
## 
## Component models: 
## '1'   '2'   '4'   '3'   '124'
## 
## Coefficients: 
##        (Intercept) Whiteness_Avg      Tint_Avg    Chroma_Avg
## full     0.7865125 -7.149858e-05 -2.574971e-05 -1.699523e-05
## subset   0.7865125 -2.405057e-04 -9.704388e-05 -6.649717e-05
##        Red_Coloration_Area
## full          1.310477e-05
## subset        5.746969e-05
summary(model.avg(out.put_modelselection))
## 
## Call:
## model.avg(object = out.put_modelselection)
## 
## Component model call: 
## lm(formula = <5 unique values>, data = body_condition_color)
## 
## Component models: 
##     df logLik   AICc delta weight
## 1    3  30.27 -53.39  0.00   0.27
## 2    3  30.14 -53.15  0.25   0.24
## 4    3  30.10 -53.06  0.33   0.23
## 3    3  30.08 -53.03  0.37   0.23
## 124  5  30.80 -48.45  4.95   0.02
## 
## Term codes: 
##       Whiteness_Avg            Tint_Avg Red_Coloration_Area          Chroma_Avg 
##                   1                   2                   3                   4 
## 
## Model-averaged coefficients:  
## (full average) 
##                       Estimate Std. Error Adjusted SE z value Pr(>|z|)    
## (Intercept)          7.865e-01  3.652e-02   3.847e-02  20.444   <2e-16 ***
## Whiteness_Avg       -7.150e-05  2.743e-04   2.848e-04   0.251    0.802    
## Tint_Avg            -2.575e-05  2.902e-04   3.067e-04   0.084    0.933    
## Chroma_Avg          -1.700e-05  1.121e-03   1.173e-03   0.014    0.988    
## Red_Coloration_Area  1.310e-05  8.810e-04   9.298e-04   0.014    0.989    
##  
## (conditional average) 
##                       Estimate Std. Error Adjusted SE z value Pr(>|z|)    
## (Intercept)          7.865e-01  3.652e-02   3.847e-02  20.444   <2e-16 ***
## Whiteness_Avg       -2.405e-04  4.609e-04   4.819e-04   0.499    0.618    
## Tint_Avg            -9.704e-05  5.572e-04   5.895e-04   0.165    0.869    
## Chroma_Avg          -6.650e-05  2.218e-03   2.320e-03   0.029    0.977    
## Red_Coloration_Area  5.747e-05  1.844e-03   1.946e-03   0.030    0.976    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
BC1 <- ggplot(body_condition_color, aes(Red_Coloration_Area, Body_Condition_Factor)) + 
  geom_point() +
  geom_smooth(method="lm")

BC2 <- ggplot(body_condition_color, aes(Whiteness_Avg, Body_Condition_Factor)) + 
  geom_point() +
  geom_smooth(method="lm")

BC3 <- ggplot(body_condition_color, aes(Chroma_Avg, Body_Condition_Factor)) + 
  geom_point() +
  geom_smooth(method="lm")

BC4 <- ggplot(body_condition_color, aes(Tint_Avg, Body_Condition_Factor)) + 
  geom_point() +
  geom_smooth(method="lm")

BC1 / BC2 / BC3 / BC4
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'

#Select models using Royall’s 1/8 rule for strength of evidence # IMPORTANT: Weights have been renormalized!!

subset(out.put_modelselection, 1/8 < weight/max(out.put_modelselection$weight))
## Model selection table 
##       (Int)    Wht_Avg    Tnt_Avg Red_Clr_Are   Chr_Avg             family df
## mod1 0.7761 -0.0001772                                  gaussian(identity)  3
## mod2 0.7866            -0.0001199                       gaussian(identity)  3
## mod4 0.7901                                   0.0002596 gaussian(identity)  3
## mod3 0.7960                         5.747e-05           gaussian(identity)  3
##      logLik  AICc delta weight
## mod1 30.268 -53.4  0.00  0.281
## mod2 30.144 -53.1  0.25  0.248
## mod4 30.103 -53.1  0.33  0.238
## mod3 30.084 -53.0  0.37  0.233
## Models ranked by AICc(x)

subset(out.put_modelselection, cumsum(out.put_modelselection$weight) <= .95)
## Model selection table 
##       (Int)    Wht_Avg    Tnt_Avg   Chr_Avg             family df logLik  AICc
## mod1 0.7761 -0.0001772                      gaussian(identity)  3 30.268 -53.4
## mod2 0.7866            -0.0001199           gaussian(identity)  3 30.144 -53.1
## mod4 0.7901                       0.0002596 gaussian(identity)  3 30.103 -53.1
##      delta weight
## mod1  0.00  0.366
## mod2  0.25  0.323
## mod4  0.33  0.310
## Models ranked by AICc(x)
sel.table2<-as.data.frame(out.put_modelselection)[6:10]

sel.table2
##                  family df   logLik      AICc     delta
## mod1 gaussian(identity)  3 30.26827 -53.39369 0.0000000
## mod2 gaussian(identity)  3 30.14440 -53.14594 0.2477518
## mod4 gaussian(identity)  3 30.10326 -53.06366 0.3300296
## mod3 gaussian(identity)  3 30.08401 -53.02516 0.3685350
## mod5 gaussian(identity)  5 30.80259 -48.44728 4.9464058
sel.table2[,2:3]<- round(sel.table2[,2:3],2)
sel.table2[2,4:5]<- round(sel.table2[,4:5],3)
## Warning in `[<-.data.frame`(`*tmp*`, 2, 4:5, value = structure(list(AICc =
## c(-53.394, : replacement element 1 has 5 rows to replace 1 rows
## Warning in `[<-.data.frame`(`*tmp*`, 2, 4:5, value = structure(list(AICc =
## c(-53.394, : replacement element 2 has 5 rows to replace 1 rows
sel.table2[,2:3]
##      df logLik
## mod1  3  30.27
## mod2  3  30.14
## mod4  3  30.10
## mod3  3  30.08
## mod5  5  30.80

names(sel.table)[1] = “K”

lets be sure to put the model names in a column

sel.table2$Model<-rownames(sel.table2)